In a spark ignition internal combustion engine, it is required that knocking does not occur. For this reason, it has been proposed to predict if knocking will occur in the current combustion cycle and, if necessary, retard the forced-ignition timing (see PLT 1).
To predict if knocking will occur, a Livengood-Wu integral which uses a formula for calculating the self-ignition delay time using the pressure and time in the cylinder as variables and considers the changes in the self-ignition delay time along with time is employed. That is, it is assumed that self-ignition occurs in the cylinder at the time when the time integral value of the reciprocal of the self-ignition delay time becomes 1, it is predicted that knocking will not occur if the combustion is completed before the timing at which the time integral value becomes 1 (all fuel in the cylinder burns), and it is predicted that knocking will occur if the combustion is not completed at the timing at which the time integral value becomes 1.